%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GRP003-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 10:51:43 EDT 2022 % Result : Unsatisfiable 4.51s 4.61s % Output : Proof 4.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP003-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n008.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue Jun 14 03:31:07 EDT 2022 % 0.12/0.33 % CPUTime : % 4.51/4.61 % SZS status Unsatisfiable % 4.51/4.61 % SZS output start Proof % 4.51/4.61 The input problem is unsatisfiable because % 4.51/4.61 % 4.51/4.61 [1] the following set of Horn clauses is unsatisfiable: % 4.51/4.61 % 4.51/4.61 product(inverse(X), X, identity) % 4.51/4.61 product(identity, X, X) % 4.51/4.61 product(X, Y, U) & product(Y, Z, V) & product(U, Z, W) ==> product(X, V, W) % 4.51/4.61 product(X, Y, U) & product(Y, Z, V) & product(X, V, W) ==> product(U, Z, W) % 4.51/4.61 product(a, identity, a) ==> \bottom % 4.51/4.61 % 4.51/4.61 This holds because % 4.51/4.61 % 4.51/4.61 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.51/4.61 % 4.51/4.61 E: % 4.51/4.61 f1(true__, X, V, W) = product(X, V, W) % 4.51/4.61 f2(true__, X, Y, U, V, W) = f1(product(X, Y, U), X, V, W) % 4.51/4.61 f3(product(U, Z, W), Y, Z, V, X, U, W) = true__ % 4.51/4.61 f3(true__, Y, Z, V, X, U, W) = f2(product(Y, Z, V), X, Y, U, V, W) % 4.51/4.61 f4(true__, U, Z, W) = product(U, Z, W) % 4.51/4.61 f5(true__, X, Y, U, Z, W) = f4(product(X, Y, U), U, Z, W) % 4.51/4.61 f6(product(X, V, W), Y, Z, V, X, U, W) = true__ % 4.51/4.61 f6(true__, Y, Z, V, X, U, W) = f5(product(Y, Z, V), X, Y, U, Z, W) % 4.51/4.61 f7(product(a, identity, a)) = true__ % 4.51/4.61 f7(true__) = false__ % 4.51/4.61 product(identity, X, X) = true__ % 4.51/4.61 product(inverse(X), X, identity) = true__ % 4.51/4.61 G: % 4.51/4.61 true__ = false__ % 4.51/4.61 % 4.51/4.61 This holds because % 4.51/4.61 % 4.51/4.61 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.51/4.61 % 4.51/4.61 % 4.51/4.61 f1(f1(true__, Y3, Y0, identity), Y3, identity, inverse(Y0)) -> true__ % 4.51/4.61 f1(f1(true__, Y3, Y2, identity), Y3, Y2, identity) -> true__ % 4.51/4.61 f1(f1(true__, Y3, Y2, inverse(identity)), Y3, Y2, identity) -> true__ % 4.51/4.61 f1(f1(true__, Y3, identity, identity), Y3, Y2, Y2) -> true__ % 4.51/4.61 f1(f1(true__, Y3, identity, inverse(Y2)), Y3, Y2, identity) -> true__ % 4.51/4.61 f1(f1(true__, Y3, inverse(Y1), identity), Y3, identity, Y1) -> true__ % 4.51/4.61 f1(f1(true__, Y3, inverse(Y1), inverse(Y1)), Y3, identity, identity) -> true__ % 4.51/4.61 f1(f1(true__, Y3, inverse(identity), identity), Y3, Y2, Y2) -> true__ % 4.51/4.61 f1(f1(true__, Y3, inverse(inverse(Y2)), identity), Y3, Y2, identity) -> true__ % 4.51/4.61 f1(true__, Y0, identity, inverse(inverse(Y0))) -> true__ % 4.51/4.61 f1(true__, Y1, identity, Y1) -> true__ % 4.51/4.61 f1(true__, Y1, inverse(Y1), identity) -> true__ % 4.51/4.61 f1(true__, identity, Y2, Y2) -> true__ % 4.51/4.61 f1(true__, identity, identity, inverse(identity)) -> true__ % 4.51/4.61 f1(true__, identity, inverse(inverse(identity)), identity) -> true__ % 4.51/4.61 f1(true__, inverse(Y1), Y1, identity) -> true__ % 4.51/4.61 f1(true__, inverse(identity), Y1, Y1) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(Y1)), identity, Y1) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(identity)), Y1, Y1) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(identity)), identity, inverse(identity)) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(inverse(Y1))), Y1, identity) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(inverse(identity))), Y1, Y1) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(inverse(inverse(Y1)))), identity, Y1) -> true__ % 4.51/4.61 f1(true__, inverse(inverse(inverse(inverse(identity)))), Y1, Y1) -> true__ % 4.51/4.61 f2(f1(true__, Y3, Y1, Y4), Y5, Y3, inverse(Y1), Y4, identity) -> true__ % 4.51/4.61 f2(f1(true__, Y3, Y2, Y4), Y5, Y3, identity, Y4, Y2) -> true__ % 4.51/4.61 f2(true__, X, Y, U, V, W) -> f1(f1(true__, X, Y, U), X, V, W) % 4.51/4.61 f3(f1(true__, Y0, Y1, Y2), Y3, Y1, Y4, Y5, Y0, Y2) -> true__ % 4.51/4.61 f3(true__, Y, Z, V, X, U, W) -> f2(f1(true__, Y, Z, V), X, Y, U, V, W) % 4.51/4.61 f4(f1(true__, identity, Y0, Y3), Y3, inverse(Y0), identity) -> true__ % 4.51/4.61 f4(f1(true__, identity, Y2, Y3), Y3, identity, Y2) -> true__ % 4.51/4.61 f4(f1(true__, identity, identity, Y3), Y3, Y2, Y2) -> true__ % 4.51/4.61 f4(f1(true__, identity, inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 4.51/4.61 f4(f1(true__, identity, inverse(identity), Y3), Y3, Y2, Y2) -> true__ % 4.51/4.61 f4(f1(true__, identity, inverse(inverse(Y2)), Y3), Y3, identity, Y2) -> true__ % 4.51/4.61 f4(f1(true__, inverse(Y2), identity, Y3), Y3, Y2, identity) -> true__ % 4.51/4.61 f4(f1(true__, inverse(identity), inverse(Y1), Y3), Y3, Y1, identity) -> true__ % 4.51/4.61 f4(true__, U, Z, W) -> f1(true__, U, Z, W) % 4.51/4.61 f5(f1(true__, Y3, Y4, Y1), inverse(Y1), Y3, Y5, Y4, identity) -> true__ % 4.51/4.61 f5(f1(true__, Y3, Y4, Y2), identity, Y3, Y5, Y4, Y2) -> true__ % 4.51/4.61 f5(true__, X, Y, U, Z, W) -> f4(f1(true__, X, Y, U), U, Z, W) % 4.51/4.61 f6(f1(true__, Y0, Y1, Y2), Y3, Y4, Y1, Y0, Y5, Y2) -> true__ % 4.51/4.61 f6(true__, Y, Z, V, X, U, W) -> f5(f1(true__, Y, Z, V), X, Y, U, Z, W) % 4.51/4.61 f7(f1(true__, a, identity, a)) -> true__ % 4.51/4.61 f7(true__) -> false__ % 4.51/4.61 false__ -> true__ % 4.51/4.61 product(X, V, W) -> f1(true__, X, V, W) % 4.51/4.61 with the LPO induced by % 4.51/4.61 f3 > f2 > f6 > f5 > f4 > product > f1 > a > inverse > identity > f7 > false__ > true__ % 4.51/4.61 % 4.51/4.61 % SZS output end Proof % 4.51/4.61 %------------------------------------------------------------------------------